Question

A bag contains 3 red, 7 black, 5 green marbles. Four marbles are selected without replacement. What is the probability that all 4 marbles are black?

Answer 1

$N=3+7+5=15$

$P(B=4)=P(B_1\cap (B_2|B_1)\cap (B_3|(B_1\cap B_2))\cap (B_4|(B_1\cap B_2\cap B_3)))$ B-black

$=\frac{7}{15}\times\frac{6}{14}\times\frac{5}{13}\times\frac{4}{12}$

$=\frac{1}{39}$